Bi-Sobolev mappings and elliptic equations in the plane

被引：38

作者：

Hencl, S. ^{[2
]}

Moscariello, G. ^{[1
]}

di Napoli, A. Passarelli ^{[1
]}

Sbordone, C. ^{[1
]}

机构：

[1] Univ Naples Federico 2, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[2] Charles Univ Prague, Dept Math Anal, Prague 18600 8, Czech Republic

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 355卷 / 01期

关键词：

Sobolev mapping; Mapping of finite distortion; FINITE DISTORTION; HOMEOMORPHISMS; REGULARITY; INVERSE;

D O I：

10.1016/j.jmaa.2009.01.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose that f = (u, v) is a homeomorphism in the plane of the Sobolev class W-loc(1,1) such that its inverse is of the same Sobolev class. We prove that u and v have the same set of critical points. As an application we show that u and v are distributional solutions to the same non-trivial degenerate elliptic equation in divergence form. We study similar properties also in higher dimensions. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：22 / 32

页数：11

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